music theory

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time 10... Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time... A dotted value may be divisible into two smaller dotted value

Music Theory

v 1.0

This is the book Music Theory (v 1.0).

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ii

About the Author 1

Acknowledgments 2

Dedication 3

Foreword 4

Preface 5

Chapter 1: The Elements of Rhythm: Sound, Symbol, and Time 9

Durational Values: Symbols Representing Time in Music 10

Pulse, Tempo, and Meter 20

Music Notation Practices 32

Additional Information 43

Summary 53

Chapter 2: The Elements of Pitch:Sound, Symbol, and Tone 54

Pitch and Pitch-Class 55

Chromatic Alteration: Accidentals 62

The Keyboard as a Visual Tool 67

Register Designation, The Octave, 8va, and 8vb 72

Pitch Notation: Nomenclature and Solfége 77

Moveable C-Clef; Other Clefs 80

Summary 86

Chapter 3: The Foundations Scale-Steps and Scales 87

Scales and Scale-Steps 88

Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale 91

Solfége Revisited 102

Heptatonic Scales: Introduction to Modes 106

Other Commonly Used Scales 113

Summary 120

Chapter 4: Key Sense, Key Signatures, and The Cycle of Fifths 121

The Sense of Key: Attributes 122

The Cycle of Fifths as a Mnemonic Device 123

Relative and Parallel Keys 124

Closely-Related Keys 125

Modes Revisited: Transposing Modes, Construction and Identification 126

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Chapter 5: Intervals 127

Simple, Compound and Multiple Intervals 128

Interval Identification Procedure: The Two Evaluative Criteria 129

The Interval Placement Diagram 130

Interval Inversion 131

Interval Construction Procedure 132

Interval Identification and Construction Below a Given Pitch 133

Chapter 6: Chords 134

Introduction and Definitions 135

The Harmonic (“Overtone”) Series 136

Triads: Four Types, Inversion, and Basic Symbolization 137

Chord Labels and Primary and Secondary Triads 138

The Conditional Status of Second Inversion Triads 139

Introduction to Seventh Chords: Five Basic Types 140

Other Common Trichords and Seventh Chords 141

Larger Chord Structures: Upper Dominant Discords and Non-Dominant Upper Extensions 142

Basic Chord Symbolization 143

Chapter 7: Basic Analytical Techniques: The Four Parameters 144

The Purpose of Analysis 145

Tonal Music: Expectation and Iteration 146

Roman Numeral Analysis (RNA) 147

The Figured Bass Tradition and its Use in Analysis 148

Categories of Chord Progressions: Expectations in Tonal Harmony 149

Chapter 8: The Cadence 150

Definition and the Sense of Closure in Music 151

Melodic Cadences 152

Final (Conclusive) and Non-Final (Inconclusive) Cadences 153

Harmonic Cadence Types 154

Procedure for Evaluating and Identifying Cadences 155

Chapter 9: Melodic Elaboration I: Non-Harmonic Activity 156

Non-Harmonic (Non-Chord) Tones 157

Types of NHT 158

Procedure for Evaluating and Identifying NHT 159

The Suspension Figure 160

iv

Expected (Typical) Use of Seventh Chords 163

Evaluating Seventh Chords in Contrast with Non-Harmonic Origins 164

Other Uses of Seventh Chords 165

Chapter 11: Chromaticism: Evaluating Tone Outside of the Prevailing Key 166

Essential versus Inessential Chromaticism 167

Modulation and Tonicization: Similarities and Contrasts 168

Modulation: Attributes and Closely Related Keys 169

Types of Modulation: Common Chord, Direct (Phrase), Chromatic, Remote, Chain 170

Tonicization: Applied Chords or Secondary Functions 171

Introduction to Altered Chords: Mode Mixture 172

Chapter 12: Formal Organization: Small Part Forms 173

Form as a Meta-Rhythm 174

The Motive: The Irreducible Creative Gesture 175

Expansion: Sub-Phrase, Phrase, Period, Double Period 176

Phrase Extension and Phrase Elision 177

Small Homophonic Part Forms: Binary, Ternary and Rounded Binary 178

Expansion and Magnification: Textbook Models of Larger Forms 179

Chapter 13: Concise Forms: Composing in the Vernacular Style 180

Characteristics of Tonal Melody 181

Common Chord Progressions 182

Argot, Jargon, and Slang in Popular Song 183

Typical Formal Patterns 184

The Blues 185

Chapter 14: The Four-Voiced Setting: The Chorale and The Chorale Setting 186

Introduction and Purpose of Study 187

SATB Chorale Style 188

Proscriptions and Prescriptions: Adherence to the Style 189

Active Tones, Voice Range, Doubling, Position 190

Chapter 15: Voice-Leading Procedures: A Positive Learning Approach 191

Introduction and Purpose of Study 192

Root Position Triads: Root Motion and Prescribed Procedures 193

Root Position Triads: Conditional Procedures 194

Triads in Inversion: Prescribed Procedures 195

Complete Procedural Table 196

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Chapter 16: “Emulative” Composition 197

Introduction and Purpose of Study 198

Realizing Simple Figured Bass in SATB 199

Realizing Simple Figured Bass in Keyboard Style 200

Procedure for Harmonizing a Given Melody 201

Chapter 17: Melodic Elaboration II Adding NHT to a Basic Setting 202

Enhancing a Setting using Appropriate Embellishment 203

Restrictions 204

The Suspension Figure: Review and Construction Procedure 205

Cadential Elaboration 206

Other NHT 207

Chapter 18: Harmonic Elaboration II: Adding Seventh Chords to a Basic Setting 208

Review and Common Use of Seventh Chords 209

Tendency Tones 210

Resolution of Seventh Chords: General Procedures for Voice Leading 211

Special Resolution Procedures 212

Chapter 19: Appendix A: Common Musical Terms 213

Chapter 20: Appendix B: Upper Dominant Discords and Non-Dominant Upper Extensions 214

Chapter 21: Appendix C: Generalized “Textbook” Models of Larger Forms 215

Chapter 22: Appendix D: Realizing Chord Changes and Some Typical Jazz Chord Voicings 216

vi

Mark Andrew Cook

Mark Andrew Cook serves as Director for Music Theory

and Composition at Shepherd University He is also a

member of the Jazz Studies Faculty Prior to his

appointment at Shepherd, he served as a member of the

Music Theory Faculty and was the Jazz Ensemble

Director at The Catholic University of America

Additionally, he served as an Adjunct Music Theory

Instructor at Towson University He also taught Music Theory, Jazz Studies, Historyand Applied subjects at Montgomery College He served as the Director of JazzEnsembles and Wind Ensemble, and as Music Director and Conductor for The

Montgomery College Symphony Orchestra In addition to teaching at ShepherdUniversity, Dr Cook is Guest Lecturer in Music Theory and Composition at TheBarbara Ingram School for the Arts

He received his B.M.ed from the Peabody Institute of the Johns Hopkins University,and both his Master’s degree and Ph.D in Music Theory from The Catholic

University of America, his dissertation being an analysis (proportional organization

and set analysis) of Paul Hindemith’s symphony Die Harmonie der Welt.

He is an active composer and performer in both the Classical and Jazz styles and hasmany performing and recording credits

1

The author would like to thank the following colleagues who have reviewed the textand provided comprehensive feedback and suggestions for improving the material:

• Kurtis Adams, Shepherd University

• Laura Renninger, Shepherd University

• David Gonzol, Shepherd University

• Scott Beard, Shepherd University

• Chris Vadala, University of Maryland, College Park

• William Hollin, The Barbara Ingram School for the Arts

• Scott Benford, Washington County (MD) Public Schools

• Michael Thorsen, Principal, The Barbara Ingram School for the Arts

• Paul Garvin Taylor, The Catholic University of America

• Steven Strunk, The Catholic University of America

• Lawren Diana Hill

In addition, a select group of instructors assisted the development of this material

by actually using it in their classrooms Their input, along with their students’feedback, has provided us critical confirmation that the material is effective in theclassroom:

2

In Memoriam

Dr Robert Wayne Ricks

He always compelled me to “take a closer look and let the Music tell its own story.”

3

This text is primarily designed to serve as a textbook for a college-level musictheory fundamentals course However, it also has the flexibility to serve equallywell for a typical core curriculum college-level Music Theory I or Harmony I course

Our goal is to deliver sufficient information to enable the student to be able toevaluate and analyze select music from the literature as quickly as is practical.Secondly, we seek to provide sufficient instruction to enable a student to beginwriting music as quickly as is practical

In order to develop a complete argument, it is important that the student

understand that this text “assumes a blank slate.” No prior knowledge on the part

of the student is assumed

In order to give Instructors greater flexibility we have intentionally providedcontent that may exceed the course objectives in some institutions We anticipatethat instructors may want to adjust the material in the text to match their currentcourse content, or adjust their courses to make use of all of the content in this text

4

The manner in which music theory has been traditionally taught is now in a state offlux Originally, the study of music theory was designed to acquaint the musicstudent or knowledgeable amateur with the composer’s working materials in

“Classical” music roughly spanning the 17th- through the 19th Centuries

The role of music theory has expanded far beyond this mandate: theory trainingnow incorporates greater or lesser explanations of music after 1900, music before

1600, idiomatic Jazz practices, elements of World Music, and Popular Song idioms

Such an expansion of means and methods in learning and teaching the fundamentallanguage of music presents a formidable and almost daunting challenge: what toteach, how to teach it, and in what sequence?

Additionally, music theory has become a favored required Arts elective in Collegeand University curricula, and most music programs have a developmental musictheory class to address the needs of under-prepared music majors Often, musictheory is required companion material for private instruction as well

This textbook seeks to address these multiple needs: to serve as a basic to moderatetext for the typical fundamentals of music course and to serve as an introductorytext for those interested in acquiring a rudimentary knowledge of the language ofmusic

The text also provides supplemental information, such as chord symbolization,aspects of Jazz harmony, vernacular song form and its attributes, and so on Usuallywhen this material is added to existing texts, it is incomplete and delivered in amanner that reflects only limited real-world experience

This author is fortunate to have had extensive experience as a teacher of musictheory at the college and university level, as a teacher of AP music theory in an ArtsMagnet high school, as a teacher of the Jazz idiom, as a practicing Classical and Jazzmusician, and as a composer in many styles

Therefore the scope of this text is to:

5

• Provide clear and concise explanations regarding the basic language ofmusic;

• Address appropriate subject matter for use by the instructor of level introductory/developmental theory courses, as well as typicalMusic Theory I courses;

college-• Add other relevant information, usually acquired informally by thestudent outside the classroom;

• Support each learning objective or skill set with reinforcement in theform of exercises;

• Prepare the student for a continuing study of music theory atintermediate to advanced levels

The format of the text and its scope will easily adapt itself to any of thesecircumstances for the instructor or for the student The modular approach and thecomplete flexibility in terms of the online access and individualized customizationenhance the facility with which the text may be employed

For example, a typical Fundamentals class may not require an examination of theSATB style and part-writing procedures In contrast, these would be critical skillsfor a Music Theory I course The Instructor can freely choose what material suits agiven need without resorting to an additional text The multiple methods of access,electronically and in print, offer both instructor and student an elastic approach tothe subject matter

Introduction

A Definition of Music

In it’s broadest possible sense, music is defined as “organized sound.” This ended and safe definition is coherent regardless of era, style, culture, or themechanics of musical organization Each successive historical era producesmusically artistic expressions of its own time, its own musical aura The study ofMusic Theory is the means by which we investigate this

open-A Definition of Music Theory

Music Theory is the study of music and its organizational characteristics We defineand examine aspects of music:

• How do we perceive music aurally?

• How do we experience music aesthetically and?

• How do we symbolize music visually?

Preface

6

We learn to associate sound with symbol (or notation), so to increase our ability toperceive music at levels of increasing depth and comprehension, both

experientially and analytically

The Purpose of Music Theory

The study of the language of music yields three unshakeable tenets:

• We learn to analyze music in order to gain an understanding of thehow great composers create We use it as a “window” into their minds,

As consumers, the more we understand about music, the more refined is our ability

to intelligently evaluate what we enjoy It is the intelligent consumer of Art who isthe greatest supporter of Art

The Means by which We Investigate Music

Examining music involves evaluation At any level of experience, this begins withpersonal taste and preference As we learn more, our method of evaluation evolves,becoming both more fluent and more critical Clearly, over time and study, thisshapes our perceptions and our tastes, regardless of what general direction thesemay take

Any study begins with an examination of fundamental precepts or principles Music

is no different The nature of perception, the basic constructs, craftsmanship inmusical construction: all must be mastered in the study of music

Two broad approaches are employed in the study of music:

• Analysis: we learn to employ commonly accepted techniques andspecialized language to describe musical organization These

7

techniques are a shared analytical language throughout thecommunity of musicians This is conceptual knowledge and evaluation.

• Composition: either by actively creating our own works, or (morelikely for the beginner), imitating or emulating the works of earliercomposers This is active knowledge and procedure

Both of these approaches will evolve as the student acquires more knowledge, skill,and greater understanding

How We Perceive Music

At the most primary level, we experience music by five principal distinctivecharacteristics

• Pitch: we perceive the sensation of sound (or tone) as relatively high orlow

• Duration: we perceive how much time sound (or silence) occupies

• Timbre: we perceive various qualities or “colors” of sound

• Intensity: we perceive differences in volume or sound pressure levels

• Events in time: we perceive pitch collections (events) in the context ofmusical space (time)

These broad generalized definitions and concepts serve us well as a departurepoint We can now progress from the general to the specific in our study

Epigraph

“The man that hath no music in himself,

Nor is not mov'd with concord of sweet sounds,

Is fit for treasons, stratagems, and spoils.”

- The Merchant of Venice (V, i)

Preface

8

The Elements of Rhythm: Sound, Symbol, and Time

Introduction

The first musical stimulus anyone reacts to is rhythm Initially, we perceive howmusic is organized in time, and how musical elements are organized rhythmically

in relation to each other Early Western music, centering upon the chant traditions

for liturgical use, was arhythmic to a great extent: the flow of the Latin text was the

principal determinant as to how the melody progressed through time

As Western music moved from monody to polyphony (“single voice” to “multiple

voices”), sets of symbols developed gradually that allowed musical time to beestablished against a recurring background pulse This also allowed multipleelements in music to be established in tandem with one another These symbols

evolved into the durational values (“note values”) that form the foundation for music

notation

9

1.1 Durational Values: Symbols Representing Time in Music

L E A R N I N G O B J E C T I V E S

1 Describing durational values orthographically: how they are drawn

2 Defining durational values in proportional relationship to one another

3 Defining durational values in musical time and space

Durational values1are symbols that represent time and action in musical space:they delineate and mark off varying values of sound (and silence) in a composition.Additionally, they are proportional to one another as to how they may be dividedfrom larger into smaller values

There have been many differing notational systems throughout the history ofmusic In the context of other study, you may encounter these various and sundrysystems from early Western notational traditions Our current system of notationevolved from these early systems, incorporating aspects of many

1 Durational Values are those

symbols (“note values”) that

are used to represent the

relative length of a particular

sound in music.

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

10

Durational Values and Proportional Chain

Below are examples of basic durational values and their common names Propernames for these values are in parentheses These names are commonly used in theUnited Kingdom and Commonwealth countries, as well as by some academics

Figure 1.2 Durational Values and Nomenclature

There are rare examples of “One-hundred and twenty-eighth-notes.” A notableexample is found in the First Movement Introduction to Beethoven’s “Pathetique”Sonata No 8, Opus 13

“Pathetique” Sonata

These occur at the end of the Introduction See this link:

http://imslp.org/wiki/Piano_Sonata_No.8,_Op.13_(Beethoven,_Ludwig_van)

Durational values are held in proportion to one another Observe that each value is

proportionally related to adjacent values If we assign the arbitrary value “1n” to a whole-note, then the half-note equals 1/2n Therefore two half-notes are required

to equal a whole note, two quarter-notes equal a half-note and so on

Figure 1.3 Durational Value Chain

Tremolo

At times notes may have a diagonal slash (or slashes) through the stem, or below anote value that has no stem These slashes are interpreted one of two ways:

1 These indicate a tremolo, the performer rapidly repeating the note, or;

2 As a notational convenience, slashes represent flags, denotingembedded smaller durational values:

Figure 1.4 Smaller Value “Slashes” (Tremolo)

These can be interpreted as “eighth-notes in the space of a half-note” (4), orsixteenth-notes in the space of a quarter,” (4) and so on This is merely a notationalconvenience employed as needed

Dotted Values

Durational values may have small periods (“dots”) appended to them Originally,this evolved as a notational “convenience,” a proportional division indication, or as

a segment boundary.Dotted values2have three different interpretations:

2 Durational Values may be

non-dotted or non-dotted Dotted Values

have three interpretations: (1)

The dot represents the

addition of half the original

value; (2) The dotted value may

divide into two lower dotted

values; (3) Or the dotted value

may divide into three

non-dotted values This potential

division into three is critical

for comprehending Compound

Meter.

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

1 A dotted value may represent the addition of half of the original

duration, or “half again as much as the original value” (“1+1/2n”).

Figure 1.5 Dotted Values: First Interpretation

2 A dotted value may be divisible into three non-dotted values:

Figure 1.6 Dotted Values: Second Interpretation

3 A dotted value may be divisible into two smaller dotted values:

Figure 1.7 Dotted Values: Third Interpretation

These varying uses of dotted values shall come into focus in subsequent discussionsconcerning meter and notational practice inSection 1.2 "Pulse, Tempo, and Meter"

andSection 1.3 "Music Notation Practices"below As with non-dotted values, dottedvalues are in proportion to one another as well.Figure 1.8 "Dotted Values"showsthe proportional chain of dotted values

Figure 1.8 Dotted Values

3 Rests are the symbols used to

represent the relative length of

silence in music They are

equivalent in value to

durations.

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

K E Y T A K E A W A Y S

The student should understand:

• Musical time is represented by symbols called durational values Theymay be dotted or non-dotted

• Durational values: specific components and specific ways how they aredrawn

• Durational values are proportional to one another

• Durational values have equivalent rest values

Durations and Rests

2 For each value given, draw three lower divisions: for example,given a whole-note, draw two half-notes, four quarter-notes,eight eighth-notes Use flags and beams (ligatures) Make sure toalign and space properly See sample solution

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

Figure 1.12

Equivalent Rests

4 For each dotted value:

a Draw the appropriate dotted lower divisions, for example, adotted half-note dividing into two dotted quarter-notes

b Draw the appropriate non-dotted lower divisions, forexample, a dotted half-note dividing into three quarter-notes

c Draw the appropriate durational values that represent theaddition of half the basic value For example, a dotted half-note is a half-note plus a quarter-note (“half again asmuch”)

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

1.2 Pulse, Tempo, and Meter

L E A R N I N G O B J E C T I V E S

1 Definitions of the elements of rhythmic organization

2 Perception of Tempo and commonly used terms

3 Mapping out meter (time signatures): the perception of Simple andCompound Time

4 How these elements interact in music

We perceive the organization of time in music in terms of three fundamental

elements, Pulse, Tempo, and Meter Use prompts to assist you in understanding these

elements:

• Pulse—“beat”: the background “heartbeat” of a piece of music.

• Tempo—“rate”: the relatively fast or slow speed at which we perceive the pulse in a piece of music.

• Meter—“ratio”: how durational values are assigned to represent the

pulse are organized in discrete segments in a piece of music.

Pulse and Tempo

Pulse4, or beat, is the regularly recurring underlying pulsation that we perceive that compels music to progress through time Pulse makes us react kinesthetically to

music: in other words, it compels motion We tap our feet, we dance, we march, or

we may just “feel” the pulse internally

In a piece of music, some durational value is assigned to be the pulse All otherdurations are proportionally related to that fundamental background pulse

Tempo5(Latin: tempus-“time”) is the rate (or relative speed) at which the pulse

flows through time This is determined by numerous methods:

1 A metronome marking: for example, MM=120 means the pulseprogresses at 120 beats per minute (two beats per second) Often, inpractice, the background durational value will be drawn and assigned a

4 Pulse (or beat) is the regularly

recurring background

pulsation in music.

5 Tempo is the rate at which we

perceive the pulse in time This

is indicated by metronome

markings, pulse value

markings and terms.

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

20

metronomic value (You will sometimes encounter the marking bpm,

“beats per minute.”)

Figure 1.15 Metronome Marking and Pulse Marking

2 Around the 17th Century (roughly!), Italian terms came to be used toindicate tempo These terms were descriptive and therefore ratherloosely interpreted as to exact tempo These terms indicate a narrow

“range” of metronomic speeds For example, the term Andante means

“going” or “a walking tempo.” This usually equates to roughly 76 beatsper minute, but may be interpreted at a slightly faster or slightlyslower pace

3 In an attempt to refine these terms, to make them more precise,

diminutives were added: Andantino indicates a slightly faster pace than

Andante Other modifiers came into common practice as well For

example, Andante con moto (“going, with motion”) is self-explanatory.

Beginning in the 19th Century, composers often used equivalent tempoand performance descriptions in their native languages, or mixedItalianate terms and vernacular terms within the same piece

4 It is important to understand that the use of these terms exceededmere indications of relative speed Often, they also carry the

connotation of style or performance practice For example, Allegro con

brio (“lively, with fire or brilliance”) implies a stylistic manner of

performance, not merely a rate at which the pulse progresses throughtime.Chapter 19 "Appendix A: Common Musical Terms"lists commonterms and their commonly accepted meanings along with someequivalents in other languages

Meter and Time SignaturesMeter6, expressed in music as a time signature, determines:

1 Which durational value is assigned to represent the fundamentalbackground pulse;

2 How these pulses are grouped together in discrete segments;

3 How these pulses naturally subdivide into lesser durational values,and;

4 The relative strength of pulses (perceived accents) within segments orgroupings of pulses.Concerning accentuation of pulse, you will

6 Meter is the “ratio” of how

many of what type of pulse

values are grouped together.

Simple Meter divides the pulse

into two equal portions;

Compound Meter divides the

pulse into three equal portions.

encounter the terms Arsis and Thesis, terms adapted from Hellenistic

poetic meter These have come to mean “upbeat” and “downbeat”

respectively These are nearly slang definitions or, at best, jargon Arsis

is best described as “preparatory,” hence perceived as a relativelyweak pulse Thesis is best described as “accentuated,” hence relativelystrong It is interesting to note that, at various times in the history ofmusic, the meaning of these two terms has been reversed from time totime

Time signatures7consist of two numbers, one over another, placed at thebeginning of a composition They may occur anywhere in a composition where ameter change is required They are NEVER written as fractions!

Simple and Compound Meter

To understand meter fully, we must first determine the fundamental nature of theprevailing background pulse or beat In given meters, we perceive beats as havingthe potential (or capacity) of being divided in two ways:

1 The prevailing background pulse may be subdivided into two

proportionally equal portions Meters having this attribute are labeled

Simple Meter (or Simple time).

2 The prevailing background pulse may be subdivided into three

proportionally equal portions Meters having this attribute are labeled

Compound Meter (Compound time).

We name meters according to two criteria:

1 Is it Simple or Compound time?

2 How many prevailing background pulses are grouped together?

Figure 1.16 Simple and Compound Divisions of Given Pulses

7 Meter is expressed as time

signatures, indicating how

many pulses (beats) are

grouped together into cogent

units.

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

So, a time signature wherein (a) the pulse subdivides into two portions, and (b) two

pulses are grouped together is called Simple Duple Three pulses grouped together,

Simple Triple and so forth A time signature wherein (a) the pulse subdivides into

three portions, and (b) two pulses are grouped together is called Compound Duple, three pulses, Compound Triple, and so forth.

Figure 1.17 Time Signatures and Labels

Simple Meter

Let us address simple meter first Analyze this by answering two questionsconcerning the stated time signature:

1 For the top number: “How many…?” In other words, how many

prevailing background pulse values (or their relative equivalent values and/or rests) are grouped together?

2 For the bottom number: “…of what kind?” In other words, what

durational value has been assigned to represent the prevailing background pulse?

So the time signature 24has two quarter-notes grouped together, therefore, we labelthis as Simple Duple

Figure 1.18 Typical Simple Meters

In Renaissance music, specialized symbols were employed that were the forerunner

of time signatures These symbols determined how relative durational values wereheld in proportion to one another We continue to employ two holdovers from thissystem

Figure 1.19 “Common Time” and “Cut Time”

“Common Time” and “Cut Time,” are slang terms Other names for “Cut Time” are

“March Time” and the proper name, Alla Breve.

The Time Signature Table

The characteristics of individual time signatures are perceived in multiple layersthat can be reduced to three basic levels:

1 The prevailing background Pulse or beat.

2 First Division: the level wherein we determine if the pulse divides into

two equal portions (simple meter) or three equal portions (compoundmeter)

3 Subdivisions: how First Division values subdivide into proportionally

smaller values

Therefore, we can graph time signatures using the following table

Table 1.1 Time Signature Table

Pulse (The fundamental background pulse.) First Division (The level determining pulse division into two portions or three portions.) Subdivisions (Subsequent divisions into smaller values.)

Figure 1.20 Time Signature Table Example

Use this table to map out time signatures and their component organizationallayers

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

a The upper number is 3 or a multiple of 3.

b The prevailing background pulse must be a dotted value:

remember, in compound meter, the pulse must have the capacity

to divide into three equal portions

c Subdivisions of the background pulse are usually grouped in sets ofthree by the use of beams (ligatures)

2 In theory, any Compound Meter may be perceived as Simple

Meter,depending upon the tempo:

a If a tempo is slow enough, any compound time signature may beperceived as a simple meter

b In practice, this is limited by style and context in compositions

3 In Compound Meter, the written time signature represents the

level of First Division,not Pulse:

a In order to find the pulse value in compound time signatures, usethe Time Signature Table List First Division values (the writtentime signature) in groupings of three

b Sum these to the dotted value representing Pulse List theseaccordingly in the Table

As with Simple time signatures, let us employ the same Time Signature Table to

graph Compound time signatures Reviewing Statement 3 above, we will follow a

slightly different procedure than that used for graphing Simple Meter:

1 For the Compound Duple time signature 68list six eighth-notes in twogroupings of three in the First Division row:

Figure 1.21 Compound Meter, First Division Groupings

2 Next, sum these groupings of three into dotted values (“two notes equal a quarter-note, the additional quarter-note represented by

eighth-a dot”); list the two resulting dotted queighth-arter-notes in the Pulse row:

Figure 1.22 Sum to Find Compound Pulse Value

3 Lastly, draw subdivisions of the First Division values in the Subdivisionrow:

Figure 1.23 Subdivision

Below are typical compound meters and their respective labels

Figure 1.24 Typical Compound Meters

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

Note that Simple meters divide all values into two subdivisions in each level of the

Table Compound meters divide the First Division level into three (see Statement 1

above) Subsequent subdivisions divide into two

Simple Triple Interpreted as Compound Meter

Some Simple Triple time signatures may be perceived as either simple orcompound, again depending upon tempo In practice, this is a limited list: The timesignatures:

may be perceived as Simple Triple if the tempo is relatively slow In other words,you perceive the “lower number” of the time signature as the fundamentalbackground pulse value As the tempo for any of these becomes relatively faster, wecease to perceive the lower number as Pulse Instead we perceive the lower number

as the First Division of a Compound meter

The Time Signature Table will show this:

Figure 1.25 Simple Triple, Compound “Single”

In the next section, these fundamental elements of sound, symbol, and time will beplaced in full musical context by uniting them with common notational practices

3

16 3 8 3 4

K E Y T A K E A W A Y S

The student should be able to define and understand:

• Pulse (“beat”), Tempo (“rate”), and Meter (“ratio”)

• Simple Meter: recognizing and analyzing Simple Time Signatures

• Compound Meter: recognizing and analyzing Compound TimeSignatures

• Time Signatures that may be perceived as either Simple or Compoundand why they are so perceived

• Using the Time Signature Table as a tool for graphing Time Signatures

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

E X E R C I S E S

1 Using the Time Signature Table, map out all examples of:

a Simple Duple and Compound Duple

Pulse First Division Subdivisions

b Simple Triple and Compound Triple

Pulse First Division Subdivisions

c Simple Quadruple and Compound Quadruple

Pulse First Division Subdivisions

Note: At the Subdivision level, draw one layer of subdivisionsonly

2 Using the Time Signature Table map out the following timesignatures as both Simple and Compound Meters:

a 316Pulse First Division

b 38Pulse First Division Subdivisions

c 68Pulse First Division Subdivisions

d 98Pulse First Division Subdivisions

3 In class (or some group), practice tapping a slow beat with your left foot.Against that beat tap two equal (“even”) divisions with your right hand(simple division) Next, keeping that same slow beat in your left foot,practice tapping three equal (“even”) divisions with your right hand(compound division) Lastly, switch hands and feet Good luck

4 The following exercises alternate between simple duple andcompound duple Tap these rhythms while keeping the sameconstant background pulse Practice each segment separately atfirst: then practice in sequence, switching from simple tocompound time as you go

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

Figure 1.26

Rhythm Drill

1.3 Music Notation Practices

L E A R N I N G O B J E C T I V E S

1 Defining and understanding measures and bar lines

2 Defining and recognizing sectional directions: “Roadmaps” in music

3 Learning basic conducting patterns

InSection 1.2 "Pulse, Tempo, and Meter", when describing meter and timesignatures, we spoke of “grouping pulse values together” to form discrete units Inmusic these groupings are delimited, or “bounded” by vertical strokes called barlines Bar lines serve as boundaries, defining a “measure” of music.For theseexamples we will employ a five-line staff Use of the staff will be explained fully in

Chapter 2 "The Elements of Pitch:Sound, Symbol, and Tone"

The crossover period between Renaissance and Baroque music at end of the 16thCentury and the beginning of the 17th Century witnessed many changes as to how

music was written The rise of the “Second Practice,” (Seconda prattica) or “New Style” (Stile moderno) of composition (early opera) and the concomitant rise of

instrumental music necessitated changes in notational practice

Since rhythmic durations in Renaissance music were organized in proportion to one

another (differing forms of mensural notation), measures and their separating bar

lines were not in use, nor were time signatures, as we know them These elementscame into gradual use Scholars offer many explanations for this: practicality andease of reading and interpretation, a shift away from multi-voiced music andtoward solo or homophonic settings in dramatic music, the desire for segmentingmusic into discrete segments, and so forth

Measure and Bar lines

This became common notational practice Ameasure8of music constituted beatgroupings (or their durational equivalents) within the context of the stated timesignature, bounded by a bar-line Composers may use a double bar line to denotesectional divisions in a piece A final bar line ends the composition

8 A measure of music is a span of

music, bounded by a bar line It

is a discrete grouping of pulse

values dictated by the time

signature.

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time

32

Figure 1.27 Measure, Bar lines, Double bar line, Final bar line

Within measures, specified beats received greater of lesser accentuation, referred to

simply as “strong” or “weak” beats This perception is based upon how the relative

strength of beats is perceived in a given time signature

Figure 1.28 Sample Time Signatures and Beat Accents

Conducting Patterns

As performers, as teachers, and as potential ensemble leaders, all musicians musthave a basic understanding of typical conducting patterns In conducting, the terms

arsis and thesis will be encountered In this context, synonyms for these terms are

“upbeat” (preparatory beat) and “downbeat” (commencement beat) The common

conducting patterns are shown inFigure 1.29 "Two-Pattern"throughFigure 1.33

Figure 1.29 Two-Pattern

All conducting figures by Michael Paolantonio

The Basic Three-Pattern: any simple triple or compound triple time signature.Think “down-away-up…”

Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time